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When using the Substitution Method to solve a system of equations, it is necessary to isolate a variable.
G
The given system consists of equations of planes. When using the Substitution Method to solve a system of equations, it is necessary to isolate a variable. In the first equation, it will be easiest to isolate x.
(I): LHS+y - z=RHS+y - z
With a variable isolated in one of the equations, we can substitute its equivalent expression into the remaining equations. In the final step of the simplification of these substitutions, our goal is to have yet another variable isolated.
(II), (III): x= y - z
This time, the y-variable was isolated in the third equation. We can now substitute its equivalent expression into the second equation.
(II): y= 11 - 2z
The value of z is 3. Substituting 3 for z into the third equation, we can find the value of y.
(III): y= 3
(III): Multiply
(III): Subtract term
Now that we know the values of y and z, we are able to find the value of x.
(I): y= 5, z= 3
(I): Subtract term
The solution of the system of three equations is the point (x, y, z). Substituting the values of x, y, and z, we know that the solution of the given system is (2,5,3). This corresponds to option G.